Free-Particle Solutions of the Dirac Equation (ALL STEPS EXPLAINED)

In this video I will find the solutions of the dirac equations, following Peskin and Schroeder's book. I will explain EVERY SINGLE STEP, and I will derive equations 3.49, 3.50, 3.59, 3.62, among others!

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My name is Nick Heumann, I am a recently graduated physicist. I love to teach physics, so I decided to give YouTube a try. English is not my first language, but I hope that you can understand me well enough regardless.
▬ Contents of this video ▬▬▬▬▬▬▬▬▬▬
00:00:00 Start
00:00:20 Finding Solutions for positive frequencies
00:02:40 Finding Rest Frame solutions
00:06:39 Applying boost in the 3 direction to energy-momentum
00:16:52 Applying boost in the 3 direction to u(p)
00:49:20 Defining the helicity operator
00:51:20 Summarizing results for u(p)
00:57:00 Finding solutions for negative frequencies
01:03:27 Important identities to know
01:06:05 Please consider supporting me on patreon!